i really dont think this is normal behavour. It sounds completely loopy to me. Like youm i dont see the problem.
If anything you were being considerate, letting her and her sister catch up. I can also understand why you felt uncomfortable, especially as its a new relationship.
I dont know what the answer to this is though...depends how much you really like her i suppose. Although i do think most men in your situation wouldn't put up with uncontrollable outbursts like that.
I t seems she has also embarassed you infron of her sister and made you look bad, which i think is dreadful.
I'm sorry you had to go through such a drama...i hope you sort things out. I'd be interested to know what happens next!